Chapter 10.1, Problem 13P

For Problems 9-17 assume that the distribution of differences d is mound-shaped and symmetric.

Please provide the following information for Problems 9-17.

(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic and corresponding t value.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?

(e) Interpret your conclusion in the context of the application.

In these problems, assume that the distribution of differences is approximately normal.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more ‘‘conservative” answer.

Wildlife: Wolves In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the United States and foreign countries. Sex ratios for eight study sites in northern Europe are shown in the following table (based on The Wolf by L. D. Mech, University of Minnesota Press).

Gender Study of Large Wolf Packs

Location of Wolf Pack	% Males (Winter)	% Males (Summer)
Finland	72	53
Finland	47	51
Finland	89	72
Lapland	55	48
Lapland	64	55
Russia	50	50
Russia	41	50
Russia	55	45

It is hypothesized that in winter, “loner" males (not present in summer packs) join the pack to increase survival rate. Use a 5% level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter.